3/8x+2=3/2x+5

Solution for 3/8x+2=3/2x+5 equation:

3/8x+2=3/2x+5

We move all terms to the left:

3/8x+2-(3/2x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

3/8x-3/2x-5+2=0

We calculate fractions


6x/16x^2+(-24x)/16x^2-5+2=0

We add all the numbers together, and all the variables

6x/16x^2+(-24x)/16x^2-3=0

We multiply all the terms by the denominator


6x+(-24x)-3*16x^2=0

Wy multiply elements

-48x^2+6x+(-24x)=0

We get rid of parentheses

-48x^2+6x-24x=0

We add all the numbers together, and all the variables

-48x^2-18x=0

a = -48; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-48)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-48}=\frac{36}{-96}
=-3/8
$